| name | quantum-structured-factorization-tomography |
| description | Unified structured factorization framework for quantum state tomography using Burer-Monteiro-type factorization parametrizing density matrix as FF†, guaranteeing physical validity while incorporating structural priors. |
| category | quantum |
| created | 2026-07-06T00:00:00.000Z |
| source | arXiv:2607.01608 |
Structured Factorization Approaches for Quantum State Tomography
Source
arXiv:2607.01608 - "Structured Factorization Approaches for Quantum State Tomography" by Zhen Qin, Joseph M. Lukens, Brian T. Kirby, Zhihui Zhu (2026-07-02)
Overview
Since quantum state tomography (QST) complexity scales exponentially with system size, exploiting priors such as low-rankness, tensor-network structures, and neural-network representations is essential for scalable QST.
Core Methodology
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Burer-Monteory Factorization: Parametrize the density matrix as FF† where factor F is constrained to belong to a structured model class.
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Physical Validity by Construction: This factorization guarantees physical validity by construction while allowing broad range of structural priors.
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Structured Model Classes: Range from generic Cholesky decomposition to low-rank matrices, matrix product states, tensor train formats, and neural network representations.
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Unified Framework: Provides single framework encompassing multiple approaches to scalable QST.
Key Findings
- Exponential complexity of QST → need for structural priors
- FF† factorization guarantees positive semidefinite density matrices
- Framework unifies low-rank, tensor network, and neural network approaches
- Enables scalable tomography in terms of both sample and parameter complexity
Applications
- Quantum state characterization in experiments
- Quantum device benchmarking
- Quantum error correction syndrome analysis
- Quantum sensing and metrology
- Quantum machine learning state preparation
Trigger Words
quantum state tomography, structured factorization, Burer-Monteiro, density matrix, low-rank, tensor network, neural network representation, sample complexity
Activation
When:
- Performing quantum state tomography
- Designing scalable quantum characterization protocols
- Working with low-rank quantum state estimation
- Using tensor network representations for quantum states
- Optimizing measurement settings for quantum state reconstruction
